A class teacher brings some clay in the classroom to teach the topic mensuration. Firstshe forms a cone of radius 10 cm and height 5 cm and then she moulds that cone into asphere.(i) Find the volume of the conical shape.(ii) Find the radius of the sphere.(iii) Find the volume of the sphere the teacher made
Question
A class teacher brings some clay in the classroom to teach the topic mensuration. Firstshe forms a cone of radius 10 cm and height 5 cm and then she moulds that cone into asphere.(i) Find the volume of the conical shape.(ii) Find the radius of the sphere.(iii) Find the volume of the sphere the teacher made
Solution
(i) The formula to find the volume of a cone is 1/3πr²h, where r is the radius and h is the height. Substituting the given values, we get:
Volume of cone = 1/3 * π * (10 cm)² * 5 cm = 500π/3 cm³
(ii) Since the clay is remoulded from the cone into a sphere, the volume of the sphere will be equal to the volume of the cone. The formula for the volume of a sphere is 4/3πr³. Setting this equal to the volume of the cone and solving for r gives:
4/3 * π * r³ = 500π/3 cm³ => r³ = (500/4) cm³ => r = ∛(125) cm => r = 5 cm
So, the radius of the sphere is 5 cm.
(iii) Now, we can find the volume of the sphere using the formula 4/3πr³:
Volume of sphere = 4/3 * π * (5 cm)³ = 500π/3 cm³
So, the volume of the sphere is also 500π/3 cm³.
Similar Questions
A spherical ball, 12 cm in diameter, is melted and cast into a conical mould, the base of which is 24 cm in diameter. What is the height of the cone?( in cm)Choices:- 4 6 8 10
7) Calculate the volume of the sphere, both in terms of p & to the nearest tenth, in which r= 3 in
A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Find the volume V of the described solid S.A frustum of a right circular cone with height h, lower base radius R, and top radius rV =
Sunita had a hemispherical bowl of radius 𝑟.She made a conical vessel of radius 𝑟 with a tinsheet.(i) find the height of the conical vessel so that it canhold the water same as that of the hemisphericalbowl.(ii) If the radius of the cone formed in the above part is 14 cm, then find how much sheet isused?(iii) If the height of the conical vessel is doubled, how much more water can it hold than thehemispherical bowl?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.